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APR vs APY Calculator
Compare Annual Percentage Rate (APR) and Annual Percentage Yield (APY) to understand the true cost of loans or returns on investments. This calculator helps you see the difference clearly based on interest rates and compounding periods.
APR vs APY Calculator
Enter the APR or APY and compounding frequency to calculate the corresponding APY or APR and understand their relationship.
Real-World Example: Comparing a Savings Account and a Credit Card
Savings Account: You deposit $10,000 into a high-yield savings account offering 5.00% APR compounded daily. The daily rate is 5.00% ÷ 365 = 0.01370%. After one year of daily compounding, your balance grows to $10,512.67. The effective APY is 5.127% — you earned $512.67 rather than the $500 you might expect from a simple 5% rate.
Credit Card: You carry a $5,000 balance on a credit card with 24.99% APR compounded daily. The daily rate is 0.0685%. After one year without payments, the balance would grow to $6,415.76. The effective APY on this debt is 28.32% — significantly higher than the advertised APR.
This example illustrates why savers should look for the highest APY (more compounding benefits them), while borrowers should pay attention to the effective APY of their debt (compounding works against them). The difference between APR and APY becomes more pronounced at higher interest rates and more frequent compounding intervals.
Formula and Methodology: APR to APY Conversion Formula
APY = (1 + APR/n)^n - 1
Where:
- APY — Annual Percentage Yield — the effective annual rate including compounding
- APR — Annual Percentage Rate — the nominal annual rate without compounding
- n — Number of compounding periods per year (12 for monthly, 365 for daily)
Worked Example
For a 5.00% APR compounded monthly: APY = (1 + 0.05/12)^12 - 1 = (1.004167)^12 - 1 = 0.05116 = 5.116%
Limitations and Assumptions
When comparing savings products, always use APY. When compounding is continuous, the formula becomes APY = e^APR - 1, where e is Euler's number (approximately 2.71828).
Scenario Comparison: APR to APY: How Compounding Frequency Changes Your Effective Rate
The same 5.00% APR produces different APYs depending on how often interest compounds.
| Compounding | Periods/Year | APY | Earnings on $10,000 |
|---|---|---|---|
| Annual | 1 | 5.000% | $500.00 |
| Semi-Annual | 2 | 5.063% | $506.25 |
| Quarterly | 4 | 5.095% | $509.45 |
| Monthly | 12 | 5.116% | $511.62 |
| Daily | 365 | 5.127% | $512.67 |
Frequently Asked Questions
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Financial Disclaimer: The content provided on this page is for informational and educational purposes only and does not constitute financial, investment, tax, or legal advice. The calculations, examples, and comparisons presented are simplified illustrations and may not reflect your specific financial situation. Always consult with a qualified financial advisor, accountant, or licensed professional before making financial decisions. Interest rates, compounding methods, and terms vary by lender and financial institution. myUSFinance is not a financial institution and does not offer loans, credit, or investment products. Past performance and hypothetical examples do not guarantee future results. Use this calculator and educational material as a starting point for your own research, not as the sole basis for any financial decision.
Understanding APR vs APY: What Every Borrower and Saver Needs to Know
When you compare financial products such as savings accounts, certificates of deposit, credit cards, or mortgage loans, two acronyms appear everywhere: APR (Annual Percentage Rate) and APY (Annual Percentage Yield). Although they sound similar, they measure fundamentally different things, and confusing the two can cost you hundreds or even thousands of dollars over the life of a financial product. This comprehensive guide breaks down the concepts so you can make smarter, more confident money decisions.
What Is APR (Annual Percentage Rate)?
APR stands for Annual Percentage Rate. It represents the yearly cost of borrowing money expressed as a simple percentage. APR includes the base interest rate plus any mandatory fees or charges imposed by the lender, such as origination fees, closing costs, or discount points on a mortgage. Importantly, APR does not take compounding into account. Because it ignores the effect of interest-on-interest, APR tends to understate the true annual cost when interest compounds more frequently than once per year. Federal law under the Truth in Lending Act (TILA) requires lenders to disclose APR so that consumers can compare loan offers on a consistent basis. You will see APR quoted on mortgages, auto loans, personal loans, student loans, and credit cards. For credit cards, the APR is typically a nominal rate that compounds daily, meaning the effective cost to the borrower is actually higher than the stated APR.
What Is APY (Annual Percentage Yield)?
APY stands for Annual Percentage Yield. Unlike APR, APY does factor in the frequency of compounding. APY tells you the real rate of return you earn on a deposit account over one year once compound interest is considered. The Federal Reserve's Regulation DD requires banks and credit unions to disclose APY on deposit products, including savings accounts, money market accounts, and CDs. Because APY accounts for compounding, it is always equal to or greater than the corresponding nominal rate. The more frequently interest compounds, the larger the gap between the nominal rate and the APY. This makes APY the better metric when comparing deposit accounts because it shows the actual yield you receive.
How Compounding Frequency Impacts Your Money
Compounding frequency is the single most important factor separating APR from APY. When a bank says it pays 5% interest compounded monthly, the bank divides 5% by 12 and applies that smaller rate each month. Each subsequent month, you earn interest not just on your original deposit but also on the interest that was added in prior months. Over the course of a year, this snowball effect results in an effective yield that exceeds the stated 5%. The same principle works against borrowers: if your credit card has a 24% APR that compounds daily, the effective annual cost is approximately 27.11%, meaning you pay significantly more than the headline number suggests. Understanding this dynamic helps you evaluate whether a seemingly attractive APR on a loan is truly competitive and whether a savings account with a slightly lower nominal rate but more frequent compounding may actually yield more.
When APR Applies vs When APY Applies
As a general rule, APR is used for borrowing (loans, credit cards, and lines of credit) while APY is used for earning (savings accounts, CDs, and money market funds). Lenders prefer to advertise APR because the number looks lower than the effective rate, making the loan appear cheaper. Banks advertising deposit products prefer to show APY because it looks higher, making their accounts appear more attractive. Savvy consumers learn to convert between the two so they can compare apples to apples. When evaluating a loan, calculate the effective annual rate (which is essentially the APY equivalent) to see the true cost. When evaluating a savings product, confirm the APY rather than the nominal rate to know your real return. By always converting to the same metric, you eliminate marketing spin and see the actual financial impact on your money.
How to Use the APR vs APY Calculator
- Enter the nominal interest rate -- This is the stated annual rate (APR) quoted by your bank or lender. For example, enter 5 if the rate is 5%.
- Select the compounding frequency -- Choose how often interest compounds: annually (1), semi-annually (2), quarterly (4), monthly (12), daily (365), or continuously. Most savings accounts compound daily or monthly; most loans compound monthly.
- Review the results -- The calculator instantly converts between APR and APY, showing the effective annual yield and the difference. Use this to compare competing offers side by side.
- Compare multiple scenarios -- Adjust the compounding frequency to see how switching from monthly to daily compounding changes your effective rate. Even a small change in frequency can make a meaningful difference over many years.
- Apply the insight -- Use the calculated APY to evaluate savings products and the effective rate to assess loan costs. This ensures you always pick the product that works hardest for your money.
The APY Formula Explained
The mathematical relationship between APR and APY is defined by the following formula:
APY = (1 + r / n)n - 1
Where r = nominal annual interest rate (as a decimal), and n = number of compounding periods per year.
Worked Example
Suppose a savings account offers a nominal rate of 5% APR compounded monthly (n = 12).
Step 1: Convert the percentage to a decimal: r = 0.05
Step 2: Divide by compounding periods: 0.05 / 12 = 0.0041667
Step 3: Add 1: 1 + 0.0041667 = 1.0041667
Step 4: Raise to the power of n: 1.004166712 = 1.05116
Step 5: Subtract 1: 1.05116 - 1 = 0.05116
Result: APY = 5.116%
This means your effective annual return is 5.116%, not 5%. On a $10,000 deposit, that difference earns you an extra $11.60 per year. Over 20 years with reinvested interest, the compounding advantage grows substantially, demonstrating why APY is the more accurate measure for savers.
APR vs APY at Different Compounding Frequencies
The table below shows how a 6% nominal APR translates into different APY values depending on how frequently interest is compounded. Notice how the APY increases as compounding becomes more frequent.
| Compounding Frequency | Periods per Year (n) | Nominal APR | Effective APY | Extra Yield on $10,000 |
|---|---|---|---|---|
| Annually | 1 | 6.000% | 6.000% | $0.00 |
| Semi-Annually | 2 | 6.000% | 6.090% | $9.00 |
| Quarterly | 4 | 6.000% | 6.136% | $13.64 |
| Monthly | 12 | 6.000% | 6.168% | $16.78 |
| Daily | 365 | 6.000% | 6.183% | $18.31 |
| Continuous | ∞ | 6.000% | 6.184% | $18.37 |
As you can see, moving from annual to daily compounding on a 6% APR adds approximately $18.31 in extra yield per $10,000 each year. While the dollar difference appears modest on small balances, it scales significantly with larger deposits and longer time horizons. On a $100,000 balance over 30 years, daily compounding versus annual compounding at the same nominal rate yields thousands of dollars more in total returns.
5 Essential Tips for Comparing APR and APY
- Always compare like with like. When evaluating loan offers, convert all rates to the same effective annual rate before comparing. A loan advertising 5.9% APR compounded daily is more expensive than one at 6.0% APR compounded annually. The headline number alone can be misleading, so perform the conversion to see the true cost.
- Ask about compounding frequency before opening an account. Two savings accounts can advertise the same nominal rate yet deliver different returns. The one that compounds daily will always beat the one compounding monthly or quarterly. Before you deposit your money, confirm the compounding schedule in the account disclosures or Truth in Savings documents.
- Watch out for introductory rates. Many credit cards and loan products offer low introductory APRs that expire after six or twelve months. Always check the ongoing rate and calculate the blended effective cost over the full term of the product. An introductory 0% APR for 12 months followed by 24.99% APR can be far more expensive than a steady 14.99% APR if you carry a balance beyond the introductory period.
- Factor in fees, not just rates. APR on a mortgage includes origination fees and points, but other products may not bundle all costs into the advertised rate. When comparing, add up all fees and calculate the total cost of borrowing or the net return after fees. A high-yield savings account with a 5.00% APY but monthly maintenance fees could yield less than a 4.80% APY account with no fees at all.
- Use time as your ally. The power of compound interest grows exponentially over time. Even a small APY advantage, when compounded over decades, produces substantial differences. Start saving early, choose accounts with competitive APY and frequent compounding, and reinvest your interest to maximize the compounding effect. The earlier and more consistently you save, the more compounding works in your favor.
Frequently Asked Questions About APR vs APY
The main difference is that APR (Annual Percentage Rate) represents the simple annual interest rate without accounting for compounding, while APY (Annual Percentage Yield) includes the effect of compound interest. APR is typically used for loans and credit products, whereas APY is used for savings and deposit accounts. Because APY factors in compounding, it always equals or exceeds the corresponding nominal APR. When comparing financial products, understanding this distinction ensures you evaluate the true cost of borrowing or the true return on savings.
APY is always higher than or equal to APR because it accounts for the compounding of interest. When interest compounds more than once per year, you earn interest on previously accumulated interest, which increases the effective annual return. The only scenario where APY equals APR is when interest compounds just once per year (annually). With monthly, daily, or continuous compounding, the APY will exceed the APR because the compounding effect generates additional returns throughout the year.
The more frequently interest compounds, the more you earn on your savings. With daily compounding, interest is calculated and added to your balance every day, meaning each subsequent day you earn interest on a slightly larger balance. Monthly compounding performs this calculation twelve times per year, while annual compounding does it just once. For a 5% nominal rate on a $10,000 deposit, daily compounding yields approximately $512.67 per year compared to $500.00 with annual compounding. Over many years, this difference compounds further, creating a significant advantage.
When comparing credit cards, pay attention to the APR because that is the rate disclosed by issuers under federal regulations. However, keep in mind that credit card interest typically compounds daily, meaning the effective annual cost (the APY equivalent) is higher than the stated APR. For example, a credit card with a 24% APR compounding daily results in an effective annual rate of about 27.11%. If you carry a balance, calculate the effective rate to understand your true cost. If you pay your balance in full each month, the APR becomes less relevant since you avoid interest charges entirely.
Yes. Use the formula: APY = (1 + r/n)^n - 1, where r is the nominal annual rate expressed as a decimal and n is the number of compounding periods per year. For example, to convert a 5% APR compounded monthly, plug in r = 0.05 and n = 12: APY = (1 + 0.05/12)^12 - 1 = approximately 0.05116, or 5.116%. You can also use our calculator above to perform this conversion instantly for any rate and compounding frequency.
Not necessarily. While a higher APY means you earn more interest on your deposits, you should also consider other factors such as minimum balance requirements, monthly maintenance fees, accessibility of funds, FDIC or NCUA insurance, withdrawal limits, and the financial stability of the institution. A savings account with a slightly lower APY but no fees and easy access may be a better choice than one with a higher APY that requires a $25,000 minimum balance or charges monthly fees that eat into your returns. Always evaluate the complete picture before choosing a savings account.
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